North Korea has vowed to accelerate its nuclear weapons programme to “maximum pace” and test a nuclear device “at any time” in response to Donald Trump’s aggressive stance towards the regime.

The warning came as US military officials said a controversial missile defence system was now “operational” after being installed at a site in South Korea last week. The Terminal High Altitude Area Defence system – or Thaad – is designed to locate and intercept North Korean missiles in mid-flight, but its deployment has been met with opposition by China and confusion over who should foot the billion-dollar bill.

US Forces Korea said Thaad was “operational and has the ability to intercept North Korean missiles and defend [South Korea]”. But a US defence official told AFP the system had only “reached initial intercept capability” and more hardware would be added later this year to make it fully functional.

North Korea vowed to continue its nuclear tests in the face of what it called US “aggression and hysteria” – a reference to joint US-South Korean military drills that the North said were taking the peninsula “to the brink of nuclear war”.

Operation Foal Eagle has just ended but the USS Carl Vinson carrier group, sent to waters off the Korean peninsula, has held exercises with the Japanese and South Korean navies in recent days.

Under controversial security laws passed in 2015, Japan on Monday sent its biggest warship to escort a US supply vessel that will later join up with the carrier group.

The Izumo, whose flight deck can accommodate up to nine helicopters, left Yokosuka port near Tokyo on Monday and will accompany the supply ship for two days as far as waters off Shikoku island in western Japan, according to the Kyodo news agency.

The US vessel is then expected to deliver fuel to the Carl Vinson and other American vessels in the region.

Tensions on the Korean peninsula have been running high, with speculation last month that North Korea would test a nuclear weapon or long-range ballistic missile – provocations that Trump warned could be met with a military response.

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Using the official name for the country, the Democratic People’s Republic of Korea (DPRK), a North Korean foreign ministry spokesman said in a statement carried by the official KCNA news agency that unless Washington ended its “hostile policy” North Korea “would continue to bolster its military capabilities for self-defence and pre-emptive nuclear attack”.

The spokesman added: “Now that the US is kicking up the overall racket for sanctions and pressure against DPRK, pursuant to its new DPRK policy called ‘maximum pressure and engagement’, the DPRK will speed up at the maximum pace the measure for bolstering its nuclear deterrence.”

The statement said “measures for bolstering the nuclear force to the maximum will be taken in a consecutive and successive way at any moment and any place decided by its supreme leadership”.

In Washington, White House spokesman Sean Spicer played down the prospect of a meeting between Trump and Kim Jong-un after the president said in an interview with Bloomberg that he would be “honoured” to hold talks with the North Korean leader under the right circumstances.

“Clearly conditions are not there right now,” Spicer said. “I don’t see this happening anytime soon.”

Senior US officials have declared an end to the era of “strategic patience” with North Korea and have not ruled out a military response if Pyongyang conducts another nuclear test or test-fires an intercontinental ballistic missile.

On Monday a US state department spokeswoman said Washington was “open to credible talks on the denuclearisation of the Korean peninsula. However, conditions must change before there is any scope for talks to resume.”